Criteria for comparison:

Smaller values of q^' result in higher quality images. At equal values of q^', it wins over the others by providing predominance of the discontinuity's amplitude over the intensity of noise. We shall restrict ourselves only to consideration of orders q^' for different situations. Earlier we introduced the order of touching of a stacking line and a travel-time curve in the case of a wave-field continuation operator. The same definition is valid for an arbitrary IG-operator. If r is the order of touching, then  

$$q^{'}=q+{1\over r+1}.$$ (140)

In order to avoid some uncertainty we shall denote the symbol v for each operator whose action depends on the choice of velocity. (This symbol may mean a scalar value or a function $v({\bf r}),v(t_{0})$ and so on). In particular, we shall write $NMO(v_{st}),{\bf P}^{x}_{w_{0}}(v_{m})$ and ${\bf P}^{s}_{w_{r}}(v_{m})$ (v_m-migration velocity, v_st-stacking velocity) . If $v_{m} \neq v_{ex}$, then operators ${\bf P}^{x}_{w_{0}}(v_{m}){\bf D}^{k}_{(-)}$ and ${\bf P}^{s}_{w_{r}}(c_{m}){\bf D}^{k}_{(-)}$ do not change the order of discontinuity. So the only reason for the inequality $q^{'}\neq q$ lies in action of operators $\sum_{s}$ and $\sum_{h}NMO(v_{st})$.